The Dell Inspiron might emit a series of beeps during start-up if the LCD cannot display errors or problems. The 8 beeps on this model indicate an '''LCD failure/an LCD cable failure'''.
If a monitor is not working it could be very likely that your Graphics chip has died which would also explain why you get no external display.
The fact it beeps at all, tells me that your BIOS is alive and you do not have a NO POST from a bad BIOS chip on the board.
You could try reseating the LCD cable, but just by the fact you get no external display, i would say this is definitely a board-level issue.
Sorry I could be of more help :(